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Tutorial

This tutorial will discuss accuracy in measurement versus precision by comparing and contrasting:

Contrasting Accuracy and Precision

1. CONTRASTING ACCURACY AND PRECISION

When talking about accuracy, the focus is how close the measurement is to what the measurement should have been.

Precision is concerned with how consistent the measurements are to each other. In other words, how close are the measurements to a single value, regardless of whether or not that single value is the right answer.

Accuracy

The extent to which the values, when considered all together, center around the correct value for a variable.

Precision

The extent to which the values are very close to each other, even if they are not near the correct value.

IN CONTEXT

You work for a consumer report company that sells personal weight scales. It’s your job to decide whether each of these scales, labeled #1, #2, #3, and #4-- are accurate, precise, both, or neither.You take someone who weighs 161.8 pounds and placed them on four different scales, five times each. Take a look at Scale #1. It has values of 160.4, 158.8, 161.4, 164.2 and 162. Determine if that's accurate, precise, both, or neither.

This scale is accurate. Why would that be? What makes these numbers “accurate”? It's accurate because the numbers average out to the right answer of 161.8.

But it reported a fairly low number such as 158.8 and a high number of 164.2, but by and large, the numbers average out to what's pretty close to the right answer.

However, Scale #1 is not precise because the number are not close to a single value every time.

Next up is Scale #2. You can tell just by looking at the numbers that all values are within 1 pound of each other, which means it is precise.

Remember, it doesn’t need to be close to the actual correct number, but they need to be close to each other. But take a look. It's overestimating by at least 7 pounds, so it's not accurate.

Take a look at Scale #3. Is it precise, accurate, both, or neither?

All of these are within a pound of each other. And they're very close to the 161.8 that is the correct value. The true weight of the individual you selected. For these reasons, having the numbers all close to each other, which make it precise, and the numbers average out to be very close to the correct weight of 161.8. Scale #3 is both accurate and precise.

Last one is Scale #4. It is neither precise nor accurate.

It actually did get the right answer once, but if you look at the five measurements taken as a whole, they're pretty far off and they tend to overestimate. They don't really center around the right number all that much, so it’s not accurate. The numbers are all over the place, so this scale is not precise.

If you worked for a consumer report company and you were evaluating scales, which scale would you choose and why?

A dartboard is a very popular example of precision and accuracy (assuming the bullseye is the desired outcome, or “value”). You can see how the top left corner is clumped together AND around the bullseye. The top right corner, they are not clumped together, but they loosely surround the bullseye. The bottom left is clumped together, but not around the correct “value”, or in this case, the bullseye. The bottom right is spread out and would not surrounding the bullseye.

By contrasting accuracy and precision, you now know that accuracy is how close the measurements are to the right answer, but not even necessarily land on the correct answer. Precision is how consistent measurements are with each other and generally you will see them clumped together. High accuracy and high precision is ideal.

Good luck!

Source: This work is adapted from Sophia author jonathan osters.

Terms to Know

Accuracy

The extent to which the values, when considered all together, center around the correct value for a variable.

Precision

The extent to which the values are very close to each other, even if they are not near the correct value.